Poster L14 - Continuous Wavelet based Transfer Function Analysis for Baroreflex Sensitivity

Introduction: Baroreflex is the most important autonomic control system that maintains arterial blood pressure within normal ranges[1]. Baroreflex evaluation is challenging in humans due to physiological fluctuation and non-stationary hemodynamic status. Cardiovagal baroreflex sensitivity (BRS) is a common parameter for accessing baroreflex function. The cardiovagal BRS shows responses of heart rate to blood pressure changes.
Transfer function analysis allows to study gain and phase relationship in the frequency domain between blood pressure (BP) and heart rate (HR). Fast Fourier Transformation (FFT) based algorithms are mostly used but cannot be applied in non-stationary data. Grinsted et al. developed an excellent continuous wavelet transformation (CWT) package with coherence and power estimations[2]. But Grinsted algorithm distorts spectral power and does not estimate transfer function[3]. The implementation of a CWT based transfer function would overcome the above limitations and opens new insight into baroreflex evaluation.
Our objective was to extend the Grinsted wavelet coherence algorithm with estimation of transfer function gain for baroreflex sensitivity assessment in humans. We tested if power and gain values estimated by our modified wavelet algorithm are not different from the FFT based transfer function for stationary signals. We hypothesized that wavelet transfer function gain can be used to detect hemodynamic fluctuation in the blood pressure control in extreme conditions.

Materials and

Methods: We performed analysis with simulated signals and real data in humans during lower body negative (LBNP) and positive pressure (LBPP).
Simulated signals
We simulated two signals consisting of two sinusoidal waves at physiological ranges (0.1 Hz and 0.25 Hz) with different phase and amplitude gain, and added white noise (0.1 variance) for 100 simulations (Figure 1).

Real data protocol
We recruited 5 healthy male subjects to study cardiovascular responses to 5-minute stepwise LBNP (-15 to -60 mmHg or maximal tolerated) and LBPP (+5 to +20 mmHg). We recorded electrocardiogram (ECG) and continuous finger BP (Finapres®, the Netherlands) and analyzed with custom written software Physiowavelab© in MATLAB (Mathworks, USA). Beat-to-beat values were interpolated, low-pass filtered (cutoff 0.4 Hz), and resampled to 5 Hz for further processing.
Simulated signals and beat-to-beat signals were transformed by FFT based Welch method and our modified Grinsted CWT method with Morlet wavelet. We corrected wavelet power using square root of wavelet scales proposed by Liu et al., 2007[3]. We calculated scale-averaged wavelet power and reconstruction factor, CDelta=0.776 (Torrence and Compo, 1998, equation 24)[4]. The following equation was used for transfer function “Txy=Pxy/Pxx”, where x is blood pressure, y is R-R interval (RRI), Pxy is smoothed cross spectral power, and Pxx is smoothed auto-spectral power. The gain was calculated as the magnitude of transfer function with applied criteria of negative phase and squared coherence value greater than 0.5. We compared power and gain obtained from FFT and modified CWT methods in low-frequency range (LF: 0.04-0.15 Hz).

Results, Conclusions, and Discussions: Results and Discussions
Simulated signals
Our modified CWT algorithm correctly detected frequency components of simulated input (x) and output signal (y) at 0.1Hz and 0.25 Hz (Figure 1 and 2). The phase plot (Axy) shows a negative phase at 0.1 Hz and positive phase at 0.25Hz (Figure 2, opposite arrows). The estimated gain was 0.5 at 0.1 Hz and 1 at 0.25Hz. High coherence values at both frequencies indicate a linear relationship (Figure 2). Averaged total power of FFT based Welch, modified CWT, and variance for x (2.562±0.026, 2.550±0.022, 2.563±0.022) and y (1.011±0.007, 1.014±0.005,1.011±0.005) were not different, which satisfy the Parseval's theorem. Dominant frequencies were also matched in the global power spectral density methods (Figure 1). Results from simulated signal validated our modified CWT method in both spectral power estimation and transfer function gain calculation.
Real data protocol
A comparison of RRI and systolic blood pressure (SBP) spectral power, coherence, and transfer function gain between the wavelet based and FFT based Welch estimation indicated good agreement between the two methods (Figure 3).
We present results in the low frequency band (LF, 0.04-0.15 Hz) of SBP and RRI because baroreflex control mainly operates in this range. Extreme blood pressure perturbation from lower body negative and positive pressure allowed us to study wide range of LF spectral power. We validated that our modified CWT method was applicable for the real physiological data.
We proposed a novel method to evaluate baroreflex function using wavelet. Wavelet transformation has advantages in that it localizes in both time and frequency, while preserving high resolution. Wavelet based baroreflex transfer function gain could be useful in non-stationary clinical tests e.g., tilt table test and Valsalva maneuver.

Conclusion
The present work provides a new method to calculate baroreflex sensitivity from wavelet-based transfer function gain which is suitable for non-stationary signals. We modified Grinsted’s CWT algorithm to fix spectral power distortion problem and added transfer function gain calculation to the algorithm. The modified code was validated with results from FFT based Welch method for both simulated and real physiological data.

Acknowledgements (Optional): André Diedrich and Surat Kulapatana were supported partly by NIH grant R01 HL142583.